# Questions tagged [kl-divergence]

For questions related to the Kullback–Leibler (KL) divergence, which is a measure (that is not a metric, but it is pre-metric, because it does not satisfy all properties of metrics, i.e. it is not symmetric) of divergence (or distance) between two probability measures (density functions, or mass functions), which is commonly used in many machine learning settings, e.g. in the context of variational auto-encoders (VAES).

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### Why has the cross-entropy become the classification standard loss function and not Kullback-Leibler divergence?

The cross-entropy is identical to the KL divergence plus the entropy of the target distribution. The KL divergence equals zero when the two distributions are the same, which seems more intuitive to me ...
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### Why is KL divergence used so often in Machine Learning?

The KL Divergence is quite easy to compute in closed form for simple distributions -such as Gaussians- but has some not-very-nice properties. For example, it is not symmetrical (thus it is not a ...
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### How is this Pytorch expression equivalent to the KL divergence?

I found the following PyTorch code (from this link) -0.5 * torch.sum(1 + sigma - mu.pow(2) - sigma.exp()) where mu is the mean ...
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### Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was ...
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### What are the advantages of the Kullback-Leibler over the MSE/RMSE?

I've recently encountered different articles that are recommending to use the KL divergence instead of the MSE/RMSE (as the loss function), when trying to learn a probability distribution, but none of ...
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### Why is the Jensen-Shannon divergence preferred over the KL divergence in measuring the performance of a generative network?

I have read articles on how Jensen-Shannon divergence is preferred over Kullback-Leibler in measuring how good a distribution mapping is learned in a generative network because of the fact that JS-...
• 1,409
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### What is the reason for mode collapse in GAN as opposed to WGAN?

In this article I am reading: $D_{KL}$ gives us inifity when two distributions are disjoint. The value of $D_{JS}$ has sudden jump, not differentiable at $\theta=0$. Only Wasserstein metric provides ...
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### What is the impact of scaling the KL divergence and reconstruction loss in the VAE objective function?

Variational autoencoders have two components in their loss function. The first component is the reconstruction loss, which for image data, is the pixel-wise difference between the input image and ...
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1 vote
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### What is the most suitable measure of the distance between two VAE's latent spaces?

The problem I'm trying to solve is as follows. I have two separate domains, where inputs do not have the same dimensions. However, I want to create a common feature space between both domains using ...
1 vote
628 views

### Why does the VAE using a KL-divergence with a non-standard mean does not produce good images?

I know I can make a VAE do generation with a mean of 0 and std-dev of 1. I tested it with the following loss function: ...
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### I don't understand how the KL Divergence works for the stated goal of Inception Score

Inception Score has two goals: The entropy for the distribution prediced on individual samples should be small(the outputs are specific) The entropy for the marginal distribution over all samples ...
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### Variational Autoencoders - Can We Learn Directly From Marginal With a Pretrained Decoder?

So, with VAE we use ELBO instead of directly maximizing the marginal likelihood, because the marginal likelihood is intractable. As far as I understand it, this is the case for two reasons: p(x) = \...
352 views

### How does one decide the probability distribution for an LLM during RLHF?

I was looking into how KL divergence is used in LLMs to prevent reward hacking within the course Generative AI with LLMs on Coursera (if this redirects to the homepage, the article is on week 3). As ...
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### How to optimize ELBO(VAE's loss function)?

Suppose we've got the following formula: \$\log p(x;\theta)=\mathbb{E}_{q(z|x;\phi)}[\log p(x,z;\theta)-\log q(z|x;\phi)]+KL(q(z|x;\phi)||p(z|x;\theta))\\ \geq \mathbb{E}_{q(z|x;\phi)}[\log p(x,z;\...
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